Difference Between Compound Interest and Simple Interest

Introduction:
Compound interest and simple interest are two different methods used to calculate the interest on a sum of money. The main difference between the two lies in how the interest is calculated and added to the principal amount. In this case, we have a sum of Rs 3000 for 3 years, with a difference of Rs 93 between compound interest and simple interest.

Simple Interest:
Simple interest is calculated by multiplying the principal amount, the rate of interest, and the time period. The formula for calculating simple interest is:

Simple Interest = (Principal * Rate * Time) / 100

In this case, the difference between compound interest and simple interest is given as Rs 93. Let's assume the rate of interest is 'r'.

Simple Interest = (3000 * r * 3) / 100

Compound Interest:
Compound interest is calculated by adding the interest earned to the principal amount at the end of each compounding period. The formula for calculating compound interest is:

Compound Interest = Principal * [(1 + Rate/100)^Time - 1]

In this case, the difference between compound interest and simple interest is given as Rs 93. Let's assume the rate of interest is 'r'.

Compound Interest = 3000 * [(1 + r/100)^3 - 1]

Equation Setup:
Now, we can set up the equation to find the rate of interest 'r' by equating the compound interest and simple interest formulas:

3000 * [(1 + r/100)^3 - 1] - (3000 * r * 3) / 100 = 93

Simplifying the equation further, we get:

3000 * (1 + r/100)^3 - 3000 * r * 3 / 100 = 93

Solving the Equation:
To solve this equation, we can use numerical methods or approximation techniques. One approach is to use the Newton-Raphson method to find the root of the equation. However, since the question does not specify the exact rate of interest, we can approximate the value by trial and error.

By trying different values of 'r' and calculating the compound interest and simple interest, we can find a value that satisfies the given condition.

Conclusion:
In summary, the difference between compound interest and simple interest on a sum of Rs 3000 for 3 years is Rs 93. The rate of interest can be determined by setting up an equation and solving it using numerical methods or approximation techniques.